**1. Introduction**

Flow and convective heat transfer through a stretching surface play an essential role in research due to their presence in many engineering and industrial applications. Many authors have emphasized this and the details are found in [1–3]. To overcome the poor thermal conductivity and increase the other thermophysical properties of the conventional fluids, nanoparticles were suspended in a base fluid. These nanoparticles are called nanofluids and can be generated from diverse operations or chemical deposition mechanisms. Enchantment in the surface area and the rate of heat transfer occurred and many improvements have recently been performed for this issue [4]. This scheme of nanofluid is processed by integrating the pure fluid and classical equations of mass. Many investigations ofnanofluid flow can be found in [5,6].

Heat transfer has been improved by adding nano-sized particles to a base fluid, as has been extensively enacted in heating and cooling methods in engineering and industries. The nano-scaled particles and the host fluid molecules are almost the same size and are identified as stable suspensions for an extended period. Convective thermal transport characteristics of nanofluids depend on the flow model, the volume fraction of nanofluid and shape of the particles [7–14]. Electronic gadgets, design of turbomachines, biomedicine, transportation, lubrication, enhanced oil recovery, lasers, petroleum drilling operations, and manufacturing process are some of the applications. The study of the combination of the fluid flow dynamic traits and the trait of electromagnetism is called magneto-hydrodynamics (MHD). It is a technique where the activities can be arrested electrically, associated with fluid flow in the presence of a magnetic flux field. The particles suspended in the fluid are controlled by the applied magnetic field and restructure their concentration; thus, the irregular heat transfer of the flow will be changed. A few situations with MHD issues are like the prediction of room climate, magneto-optical wavelength filters, estimations of stream rates of refreshments in the nourishment industry, optical switches and optical modulators. Magneto-nanoparticles are highly used in cancer therapy, MRI, magnetic drug targeting, hyperthermia, magnetic cell separation and drug delivery. They likewise have uses in geophysics; this is connected to thinking about stellar and solar structures, design of MHD pumps, etc. Several other significant investigations in this concern are due to [15–21].

Finally, Lie-group methods and their invariants o ffer a powerful, sophisticated, and methodical technique to obtain group-invariant solutions which are called self-similarity transformations. Self-similarity transformations achieved reduction of the independent variable numbers of a set of PDEs, leading to conversion of the non-linear governing PDEs into ODEs. Analysis using Lie groups has been executed by many scientists and applied mathematicians in many investigations [22–28].

In the current work, we analyze the unsteady MHD flow of ferrofluid and convective heat transfer confined by a radiate stretched sheet with the influence of Navier slip and convective heating. The mathematical model was solved numerically with the aid of Runge–Kutta–Fehlberg method. The aspects of various parameters such as velocity, temperature, shear stress fields and skin friction coe fficient parameters associated with the current analysis are graphically examined. The recent advancements in modern technology have stimulated research interest in the analysis of boundary layer ferrofluid flow overstretching surfaces for its use in various engineering and industrial applications, such as paper production, fiberglass production, several engineering processes like solar power technology, etc.
